public class MaxFlowPreflowN3 { int[][] cap; public void init(int nodes) { cap = new int[nodes][nodes]; } public void addEdge(int s, int t, int capacity) { cap[s][t] = capacity; } public int maxFlow(int s, int t) { int n = cap.length; int[] h = new int[n]; h[s] = n - 1; int[] maxh = new int[n]; int[][] f = new int[n][n]; int[] e = new int[n]; for (int i = 0; i < n; ++i) { f[s][i] = cap[s][i]; f[i][s] = -f[s][i]; e[i] = cap[s][i]; } for (int sz = 0;;) { if (sz == 0) { for (int i = 0; i < n; ++i) if (i != s && i != t && e[i] > 0) { if (sz != 0 && h[i] > h[maxh[0]]) sz = 0; maxh[sz++] = i; } } if (sz == 0) break; while (sz != 0) { int i = maxh[sz - 1]; boolean pushed = false; for (int j = 0; j < n && e[i] != 0; ++j) { if (h[i] == h[j] + 1 && cap[i][j] - f[i][j] > 0) { int df = Math.min(cap[i][j] - f[i][j], e[i]); f[i][j] += df; f[j][i] -= df; e[i] -= df; e[j] += df; if (e[i] == 0) --sz; pushed = true; } } if (!pushed) { h[i] = Integer.MAX_VALUE; for (int j = 0; j < n; ++j) if (h[i] > h[j] + 1 && cap[i][j] - f[i][j] > 0) h[i] = h[j] + 1; if (h[i] > h[maxh[0]]) { sz = 0; break; } } } } int flow = 0; for (int i = 0; i < n; i++) flow += f[s][i]; return flow; } // Usage example public static void main(String[] args) { int[][] capacity = { { 0, 3, 2 }, { 0, 0, 2 }, { 0, 0, 0 } }; int n = capacity.length; MaxFlowPreflowN3 flow = new MaxFlowPreflowN3(); flow.init(n); for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (capacity[i][j] != 0) flow.addEdge(i, j, capacity[i][j]); System.out.println(4 == flow.maxFlow(0, 2)); } }